| 1 | C71×#3058 | C2 | 1 | 1 | yes | maximal, characteristic |
| 2 | C71×#2155 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 3 | C2×#361×C71 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 4 | C71×#2140 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 5 | C71×#2117 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 6 | C71×#1814 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 7 | C71×#1384 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 8 | C22×D8×C71 | C22 | 1 | 1 | yes | characteristic |
| 9 | C2×#131×C71 | C22 | 1 | 1 | yes | characteristic |
| 10 | #535×C71 | — | 2 | 1 | no | — |
| 11 | C2×M32×C71 | C22 | 1 | 1 | yes | characteristic |
| 12 | C2×M32×C71 | C22 | 1 | 1 | yes | characteristic |
| 13 | #469×C71 | — | 2 | 2 | no | — |
| 14 | #466×C71 | — | 2 | 2 | no | — |
| 15 | C2×#108×C71 | C22 | 1 | 1 | yes | characteristic |
| 16 | #427×C71 | C22 | 1 | 1 | yes | characteristic |
| 17 | #427×C71 | C22 | 1 | 1 | yes | characteristic |
| 18 | #421×C71 | — | 2 | 1 | no | — |
| 19 | #418×C71 | — | 2 | 1 | no | — |
| 20 | #365×C71 | — | 2 | 2 | no | — |
| 21 | #361×C71 | — | 2 | 2 | no | — |
| 22 | #357×C71 | — | 2 | 2 | no | — |
| 23 | #350×C71 | — | 2 | 2 | no | — |
| 24 | #344×C71 | — | 2 | 1 | no | — |
| 25 | C2×#41×C71 | D4 | 1 | 1 | yes | characteristic |
| 26 | C22×D4×C71 | — | 2 | 1 | no | — |
| 27 | C2×D8×C71 | — | 2 | 1 | no | — |
| 28 | C2×D8×C71 | — | 2 | 1 | no | — |
| 29 | C2×D8×C71 | — | 2 | 1 | no | — |
| 30 | C2×D8×C71 | — | 2 | 1 | no | — |
| 31 | C2×D8×C71 | — | 2 | 1 | no | — |
| 32 | C2×D8×C71 | D4 | 1 | 2 | yes | — |
| 33 | #131×C71 | — | 2 | 1 | no | — |
| 34 | #131×C71 | — | 2 | 1 | no | — |
| 35 | #131×C71 | — | 2 | 1 | no | — |
| 36 | #131×C71 | — | 2 | 1 | no | — |
| 37 | C2×M16×C71 | — | 2 | 1 | no | — |
| 38 | C2×M16×C71 | — | 2 | 1 | no | — |
| 39 | C2×M16×C71 | D4 | 1 | 1 | yes | characteristic |
| 40 | C22×C8×C71 | — | 2 | 1 | no | — |
| 41 | C22×C8×C71 | C23 | 1 | 1 | yes | characteristic |
| 42 | #127×C71 | — | 4 | 1 | no | — |
| 43 | #124×C71 | — | 4 | 1 | no | — |
| 44 | #121×C71 | — | 2 | 4 | no | — |
| 45 | #120×C71 | — | 4 | 2 | no | — |
| 46 | #117×C71 | — | 2 | 1 | no | — |
| 47 | #117×C71 | — | 2 | 1 | no | — |
| 48 | M32×C71 | — | 2 | 1 | no | — |
| 49 | M32×C71 | — | 2 | 1 | no | — |
| 50 | M32×C71 | — | 2 | 1 | no | — |
| 51 | M32×C71 | — | 2 | 1 | no | — |
| 52 | C2×C16×C71 | — | 2 | 1 | no | — |
| 53 | C2×C16×C71 | D4 | 1 | 2 | yes | complemented |
| 54 | #108×C71 | — | 2 | 1 | no | — |
| 55 | #108×C71 | — | 2 | 1 | no | — |
| 56 | #107×C71 | — | 2 | 1 | no | — |
| 57 | #107×C71 | — | 2 | 1 | no | — |
| 58 | #106×C71 | — | 2 | 1 | no | — |
| 59 | #106×C71 | D4 | 1 | 2 | yes | — |
| 60 | #104×C71 | — | 4 | 2 | no | — |
| 61 | #102×C71 | — | 2 | 4 | no | — |
| 62 | C24×C71 | — | 4 | 1 | no | — |
| 63 | #41×C71 | — | 2 | 1 | no | — |
| 64 | #41×C71 | — | 2 | 1 | no | — |
| 65 | #41×C71 | — | 2 | 1 | no | — |
| 66 | #41×C71 | — | 2 | 1 | no | — |
| 67 | C2×Q8×C71 | SD16 | 1 | 1 | yes | characteristic |
| 68 | C2×D4×C71 | — | 2 | 1 | no | — |
| 69 | C2×D4×C71 | — | 2 | 2 | no | — |
| 70 | C2×D4×C71 | — | 4 | 4 | no | — |
| 71 | C2×D4×C71 | — | 4 | 1 | no | — |
| 72 | C2×D4×C71 | — | 4 | 1 | no | — |
| 73 | C2×D4×C71 | — | 4 | 1 | no | — |
| 74 | C2×D4×C71 | — | 4 | 1 | no | — |
| 75 | C2×D4×C71 | — | 4 | 1 | no | — |
| 76 | C2×D4×C71 | SD16 | 1 | 1 | yes | characteristic |
| 77 | C22×C4×C71 | — | 2 | 1 | no | — |
| 78 | C22×C4×C71 | C2×D4 | 1 | 1 | yes | characteristic |
| 79 | D8×C71 | — | 2 | 2 | no | — |
| 80 | D8×C71 | — | 2 | 2 | no | — |
| 81 | D8×C71 | — | 4 | 1 | no | — |
| 82 | D8×C71 | — | 4 | 1 | no | — |
| 83 | M16×C71 | — | 2 | 1 | no | — |
| 84 | M16×C71 | — | 2 | 1 | no | — |
| 85 | M16×C71 | — | 4 | 1 | no | — |
| 86 | M16×C71 | — | 4 | 1 | no | — |
| 87 | M16×C71 | — | 4 | 1 | no | — |
| 88 | M16×C71 | — | 4 | 1 | no | — |
| 89 | C2×C8×C71 | — | 2 | 1 | no | — |
| 90 | C2×C8×C71 | — | 4 | 1 | no | — |
| 91 | C2×C8×C71 | — | 4 | 1 | no | — |
| 92 | C2×C8×C71 | — | 4 | 1 | no | — |
| 93 | C2×C8×C71 | C2×D4 | 1 | 1 | yes | characteristic |
| 94 | C2×C8×C71 | C2×D4 | 1 | 1 | yes | characteristic |
| 95 | C2×C8×C71 | C2×D4 | 1 | 1 | yes | characteristic |
| 96 | C2×C8×C71 | #41 | 1 | 1 | yes | characteristic |
| 97 | C2×C8×C71 | #41 | 1 | 1 | yes | characteristic |
| 98 | C2×C8×C71 | #41 | 1 | 1 | yes | characteristic |
| 99 | C4⋊C4×C71 | — | 2 | 2 | no | — |
| 100 | C4⋊C4×C71 | — | 4 | 1 | no | — |
| 101 | C22⋊C4×C71 | — | 4 | 4 | no | — |
| 102 | C22⋊C4×C71 | — | 4 | 1 | no | — |
| 103 | C22⋊C4×C71 | — | 4 | 1 | no | — |
| 104 | C42×C71 | — | 4 | 1 | no | — |
| 105 | C42×C71 | — | 4 | 1 | no | — |
| 106 | C16×C71 | — | 2 | 2 | no | — |
| 107 | C16×C71 | — | 4 | 1 | no | — |
| 108 | C23×C71 | — | 2 | 1 | no | — |
| 109 | C23×C71 | — | 4 | 2 | no | — |
| 110 | C23×C71 | — | 8 | 1 | no | — |
| 111 | C23×C71 | — | 8 | 1 | no | — |
| 112 | C23×C71 | — | 16 | 2 | no | — |
| 113 | C23×C71 | AGL(1,ℤ/8) | 1 | 1 | yes | characteristic |
| 114 | Q8×C71 | — | 2 | 1 | no | — |
| 115 | Q8×C71 | — | 2 | 1 | no | — |
| 116 | D4×C71 | — | 2 | 1 | no | — |
| 117 | D4×C71 | — | 2 | 1 | no | — |
| 118 | D4×C71 | — | 4 | 1 | no | — |
| 119 | D4×C71 | — | 4 | 1 | no | — |
| 120 | D4×C71 | — | 4 | 2 | no | — |
| 121 | D4×C71 | — | 4 | 2 | no | — |
| 122 | D4×C71 | — | 8 | 1 | no | — |
| 123 | D4×C71 | — | 8 | 1 | no | — |
| 124 | D4×C71 | — | 16 | 4 | no | — |
| 125 | C2×C4×C71 | — | 2 | 1 | no | — |
| 126 | C2×C4×C71 | — | 4 | 1 | no | — |
| 127 | C2×C4×C71 | — | 4 | 1 | no | — |
| 128 | C2×C4×C71 | — | 4 | 2 | no | — |
| 129 | C2×C4×C71 | — | 8 | 1 | no | — |
| 130 | C2×C4×C71 | #120 | 1 | 1 | yes | characteristic |
| 131 | C2×C4×C71 | #121 | 1 | 1 | yes | characteristic |
| 132 | C2×C4×C71 | #123 | 1 | 1 | yes | characteristic |
| 133 | C2×C4×C71 | C2×SD16 | 1 | 1 | yes | characteristic |
| 134 | C2×C4×C71 | #135 | 1 | 1 | yes | characteristic |
| 135 | C2×C4×C71 | AGL(1,ℤ/8) | 1 | 1 | yes | characteristic |
| 136 | C8×C71 | — | 4 | 1 | no | — |
| 137 | C8×C71 | — | 8 | 1 | no | — |
| 138 | C8×C71 | #121 | 1 | 1 | yes | characteristic |
| 139 | C8×C71 | #121 | 1 | 1 | yes | characteristic |
| 140 | C8×C71 | #123 | 1 | 1 | yes | characteristic |
| 141 | C8×C71 | #124 | 1 | 1 | yes | characteristic |
| 142 | C22×C71 | — | 4 | 1 | no | — |
| 143 | C22×C71 | — | 4 | 2 | no | — |
| 144 | C22×C71 | — | 4 | 1 | no | — |
| 145 | C22×C71 | — | 8 | 4 | no | — |
| 146 | C22×C71 | — | 8 | 2 | no | — |
| 147 | C22×C71 | — | 16 | 2 | no | — |
| 148 | C22×C71 | — | 16 | 2 | no | — |
| 149 | C22×C71 | #450 | 1 | 1 | yes | characteristic |
| 150 | C22×C71 | #469 | 1 | 1 | yes | characteristic |
| 151 | C22×C71 | #482 | 1 | 1 | yes | characteristic |
| 152 | C4×C71 | — | 4 | 1 | no | — |
| 153 | C4×C71 | — | 8 | 2 | no | — |
| 154 | C4×C71 | — | 16 | 1 | no | — |
| 155 | C4×C71 | #394 | 1 | 1 | yes | characteristic |
| 156 | C4×C71 | #449 | 1 | 1 | yes | characteristic |
| 157 | C4×C71 | #465 | 1 | 1 | yes | characteristic |
| 158 | C4×C71 | #481 | 1 | 1 | yes | characteristic |
| 159 | #13396 | C71 | 1 | 1 | yes | maximal, characteristic, direct product factor, Sylow |
| 160 | C2×C71 | — | 2 | 1 | no | — |
| 161 | C2×C71 | — | 2 | 1 | no | — |
| 162 | C2×C71 | — | 2 | 1 | no | — |
| 163 | C2×C71 | — | 8 | 1 | no | — |
| 164 | C2×C71 | — | 16 | 2 | no | — |
| 165 | C2×C71 | #2034 | 1 | 1 | yes | characteristic |
| 166 | #3058 | C2×C71 | 1 | 1 | yes | characteristic |
| 167 | #2155 | C2×C71 | 1 | 1 | yes | characteristic, complemented |
| 168 | C2×#361 | C2×C71 | 1 | 1 | yes | characteristic, complemented |
| 169 | #2140 | C2×C71 | 1 | 1 | yes | characteristic, complemented |
| 170 | #2117 | C2×C71 | 1 | 1 | yes | characteristic, complemented |
| 171 | #1814 | C2×C71 | 1 | 1 | yes | characteristic, complemented |
| 172 | #1384 | C2×C71 | 1 | 1 | yes | characteristic, complemented |
| 173 | C71 | #13396 | 1 | 1 | yes | characteristic, direct product factor, Sylow |
| 174 | C22×D8 | C22×C71 | 1 | 1 | yes | characteristic |
| 175 | C2×#131 | C22×C71 | 1 | 1 | yes | characteristic |
| 176 | #535 | — | 2 | 1 | no | — |
| 177 | C2×M32 | C22×C71 | 1 | 1 | yes | characteristic |
| 178 | C2×M32 | C22×C71 | 1 | 1 | yes | characteristic |
| 179 | #469 | — | 2 | 2 | no | — |
| 180 | #466 | — | 2 | 2 | no | — |
| 181 | C2×#108 | C22×C71 | 1 | 1 | yes | characteristic |
| 182 | #427 | C22×C71 | 1 | 1 | yes | characteristic |
| 183 | #427 | C22×C71 | 1 | 1 | yes | characteristic |
| 184 | #421 | — | 2 | 1 | no | — |
| 185 | #418 | — | 2 | 1 | no | — |
| 186 | #365 | — | 2 | 2 | no | — |
| 187 | #361 | — | 2 | 2 | no | — |
| 188 | #357 | — | 2 | 2 | no | — |
| 189 | #350 | — | 2 | 2 | no | — |
| 190 | #344 | — | 2 | 1 | no | — |
| 191 | C2×#41 | D4×C71 | 1 | 1 | yes | characteristic |
| 192 | C22×D4 | — | 2 | 1 | no | — |
| 193 | C2×D8 | — | 2 | 1 | no | — |
| 194 | C2×D8 | — | 2 | 1 | no | — |
| 195 | C2×D8 | — | 2 | 1 | no | — |
| 196 | C2×D8 | — | 2 | 1 | no | — |
| 197 | C2×D8 | — | 2 | 1 | no | — |
| 198 | C2×D8 | D4×C71 | 1 | 2 | yes | — |
| 199 | #131 | — | 2 | 1 | no | — |
| 200 | #131 | — | 2 | 1 | no | — |
| 201 | #131 | — | 2 | 1 | no | — |
| 202 | #131 | — | 2 | 1 | no | — |
| 203 | C2×M16 | — | 2 | 1 | no | — |
| 204 | C2×M16 | — | 2 | 1 | no | — |
| 205 | C2×M16 | D4×C71 | 1 | 1 | yes | characteristic |
| 206 | C22×C8 | — | 2 | 1 | no | — |
| 207 | C22×C8 | C23×C71 | 1 | 1 | yes | characteristic |
| 208 | #127 | — | 4 | 1 | no | — |
| 209 | #124 | — | 4 | 1 | no | — |
| 210 | #121 | — | 2 | 4 | no | — |
| 211 | #120 | — | 4 | 2 | no | — |
| 212 | #117 | — | 2 | 1 | no | — |
| 213 | #117 | — | 2 | 1 | no | — |
| 214 | M32 | — | 2 | 1 | no | — |
| 215 | M32 | — | 2 | 1 | no | — |
| 216 | M32 | — | 2 | 1 | no | — |
| 217 | M32 | — | 2 | 1 | no | — |
| 218 | C2×C16 | — | 2 | 1 | no | — |
| 219 | C2×C16 | D4×C71 | 1 | 2 | yes | complemented |
| 220 | #108 | — | 2 | 1 | no | — |
| 221 | #108 | — | 2 | 1 | no | — |
| 222 | #107 | — | 2 | 1 | no | — |
| 223 | #107 | — | 2 | 1 | no | — |
| 224 | #106 | — | 2 | 1 | no | — |
| 225 | #106 | D4×C71 | 1 | 2 | yes | — |
| 226 | #104 | — | 4 | 2 | no | — |
| 227 | #102 | — | 2 | 4 | no | — |
| 228 | C24 | — | 4 | 1 | no | — |
| 229 | #41 | — | 2 | 1 | no | — |
| 230 | #41 | — | 2 | 1 | no | — |
| 231 | #41 | — | 2 | 1 | no | — |
| 232 | #41 | — | 2 | 1 | no | — |
| 233 | C2×Q8 | SD16×C71 | 1 | 1 | yes | characteristic |
| 234 | C2×D4 | — | 2 | 1 | no | — |
| 235 | C2×D4 | — | 2 | 2 | no | — |
| 236 | C2×D4 | — | 4 | 4 | no | — |
| 237 | C2×D4 | — | 4 | 1 | no | — |
| 238 | C2×D4 | — | 4 | 1 | no | — |
| 239 | C2×D4 | — | 4 | 1 | no | — |
| 240 | C2×D4 | — | 4 | 1 | no | — |
| 241 | C2×D4 | — | 4 | 1 | no | — |
| 242 | C2×D4 | SD16×C71 | 1 | 1 | yes | characteristic |
| 243 | C22×C4 | — | 2 | 1 | no | — |
| 244 | C22×C4 | C2×D4×C71 | 1 | 1 | yes | characteristic |
| 245 | D8 | — | 2 | 2 | no | — |
| 246 | D8 | — | 2 | 2 | no | — |
| 247 | D8 | — | 4 | 1 | no | — |
| 248 | D8 | — | 4 | 1 | no | — |
| 249 | M16 | — | 2 | 1 | no | — |
| 250 | M16 | — | 2 | 1 | no | — |
| 251 | M16 | — | 4 | 1 | no | — |
| 252 | M16 | — | 4 | 1 | no | — |
| 253 | M16 | — | 4 | 1 | no | — |
| 254 | M16 | — | 4 | 1 | no | — |
| 255 | C2×C8 | — | 2 | 1 | no | — |
| 256 | C2×C8 | — | 4 | 1 | no | — |
| 257 | C2×C8 | — | 4 | 1 | no | — |
| 258 | C2×C8 | — | 4 | 1 | no | — |
| 259 | C2×C8 | C2×D4×C71 | 1 | 1 | yes | characteristic |
| 260 | C2×C8 | C2×D4×C71 | 1 | 1 | yes | characteristic |
| 261 | C2×C8 | C2×D4×C71 | 1 | 1 | yes | characteristic |
| 262 | C2×C8 | #41×C71 | 1 | 1 | yes | characteristic |
| 263 | C2×C8 | #41×C71 | 1 | 1 | yes | characteristic |
| 264 | C2×C8 | #41×C71 | 1 | 1 | yes | characteristic |
| 265 | C4⋊C4 | — | 2 | 2 | no | — |
| 266 | C4⋊C4 | — | 4 | 1 | no | — |
| 267 | C22⋊C4 | — | 4 | 4 | no | — |
| 268 | C22⋊C4 | — | 4 | 1 | no | — |
| 269 | C22⋊C4 | — | 4 | 1 | no | — |
| 270 | C42 | — | 4 | 1 | no | — |
| 271 | C42 | — | 4 | 1 | no | — |
| 272 | C16 | — | 2 | 2 | no | — |
| 273 | C16 | — | 4 | 1 | no | — |
| 274 | C23 | — | 2 | 1 | no | — |
| 275 | C23 | — | 4 | 2 | no | — |
| 276 | C23 | — | 8 | 1 | no | — |
| 277 | C23 | — | 8 | 1 | no | — |
| 278 | C23 | — | 16 | 2 | no | — |
| 279 | C23 | AGL(1,ℤ/8)×C71 | 1 | 1 | yes | characteristic |
| 280 | Q8 | — | 2 | 1 | no | — |
| 281 | Q8 | — | 2 | 1 | no | — |
| 282 | D4 | — | 2 | 1 | no | — |
| 283 | D4 | — | 2 | 1 | no | — |
| 284 | D4 | — | 4 | 1 | no | — |
| 285 | D4 | — | 4 | 1 | no | — |
| 286 | D4 | — | 4 | 2 | no | — |
| 287 | D4 | — | 4 | 2 | no | — |
| 288 | D4 | — | 8 | 1 | no | — |
| 289 | D4 | — | 8 | 1 | no | — |
| 290 | D4 | — | 16 | 4 | no | — |
| 291 | C2×C4 | — | 2 | 1 | no | — |
| 292 | C2×C4 | — | 4 | 1 | no | — |
| 293 | C2×C4 | — | 4 | 1 | no | — |
| 294 | C2×C4 | — | 4 | 2 | no | — |
| 295 | C2×C4 | — | 8 | 1 | no | — |
| 296 | C2×C4 | #120×C71 | 1 | 1 | yes | characteristic |
| 297 | C2×C4 | #121×C71 | 1 | 1 | yes | characteristic |
| 298 | C2×C4 | #123×C71 | 1 | 1 | yes | characteristic |
| 299 | C2×C4 | C2×SD16×C71 | 1 | 1 | yes | characteristic |
| 300 | C2×C4 | #135×C71 | 1 | 1 | yes | characteristic |
| 301 | C2×C4 | AGL(1,ℤ/8)×C71 | 1 | 1 | yes | characteristic |
| 302 | C8 | — | 4 | 1 | no | — |
| 303 | C8 | — | 8 | 1 | no | — |
| 304 | C8 | #121×C71 | 1 | 1 | yes | characteristic |
| 305 | C8 | #121×C71 | 1 | 1 | yes | characteristic |
| 306 | C8 | #123×C71 | 1 | 1 | yes | characteristic |
| 307 | C8 | #124×C71 | 1 | 1 | yes | characteristic |
| 308 | C22 | — | 4 | 1 | no | — |
| 309 | C22 | — | 4 | 2 | no | — |
| 310 | C22 | — | 4 | 1 | no | — |
| 311 | C22 | — | 8 | 4 | no | — |
| 312 | C22 | — | 8 | 2 | no | — |
| 313 | C22 | — | 16 | 2 | no | — |
| 314 | C22 | — | 16 | 2 | no | — |
| 315 | C22 | #450×C71 | 1 | 1 | yes | characteristic |
| 316 | C22 | #469×C71 | 1 | 1 | yes | characteristic |
| 317 | C22 | #482×C71 | 1 | 1 | yes | characteristic |
| 318 | C4 | — | 4 | 1 | no | — |
| 319 | C4 | — | 8 | 2 | no | — |
| 320 | C4 | — | 16 | 1 | no | — |
| 321 | C4 | #394×C71 | 1 | 1 | yes | characteristic |
| 322 | C4 | #449×C71 | 1 | 1 | yes | characteristic |
| 323 | C4 | #465×C71 | 1 | 1 | yes | characteristic |
| 324 | C4 | #481×C71 | 1 | 1 | yes | characteristic |
| 325 | C2 | — | 2 | 1 | no | — |
| 326 | C2 | — | 2 | 1 | no | — |
| 327 | C2 | — | 2 | 1 | no | — |
| 328 | C2 | — | 8 | 1 | no | — |
| 329 | C2 | — | 16 | 2 | no | — |
| 330 | C2 | C71×#2034 | 1 | 1 | yes | characteristic |
Finite Group Databasebeta